The center of mass (or centroid) of a rigid body is
found by averaging the spatial points of the body
weighted by the mass
of those points:B.12

Thus, the center of mass is the mass-weighted average location
of the object. For a continuous mass distribution totaling up to
,
we can write

where the volume integral is taken over a volume
of 3D space that
includes the rigid body, and
denotes the mass contained within the differential volume
element
located at the point
, with
denoting the mass density at the point
. The total mass
is

A nice property of the center of mass is that gravity acts on a
far-away object as if all its mass were concentrated at its center of
mass. For this reason, the center of mass is often called the
center of gravity.